Futures Options - OER University - Anvari.Netcbafaculty.org/Futures and Options... · PPT file · Web view · 2017-04-18Futures Options and Black’s Model. Chapter 16. Options

Fundamentals of Futures and Options Markets, 9th Ed, Ch 16, Copyright © John C. Hull 2016

Futures Options and Black’s Model

Chapter 16

1

Options on FuturesReferred to by the maturity month of the

underlying futures The option is American and usually

expires on or a few days before the earliest delivery date of the underlying futures contract


2


Mechanics of Call Futures Options

When a call futures option is exercised the holder acquires

1. A long position in the futures2. A cash amount equal to the excess of the

futures price at the most recent settlement over the strike price

3


Mechanics of Put Futures Option

When a put futures option is exercised the holder acquires

1. A short position in the futures2. A cash amount equal to the excess of the strike

price over the futures price at the most recent settlement

4

Example 16.1 (page 345)

July call option contract on gold futures has a strike of $1200 per ounce. It is exercised when futures price is $1,240 and most recent settlement is $1,238. One contract is on 100 ounces

Trader receives Long July futures contract on gold $3,800 in cash


5

Example 16.2 (page 346)

Sept put option contract on corn futures has a strike price of 300 cents per bushel.

It is exercised when the futures price is 280 cents per bushel and the most recent settlement price is 279 cents per bushel. One contract is on 5000 bushels

Trader receives Short Sept futures contract on corn $1,050 in cash


6


The Payoffs

If the futures position is closed out immediately:Payoff from call = F – KPayoff from put = K – Fwhere F is futures price at time of exercise

7


Potential Advantages of FuturesOptions over Spot Options

Futures contract may be easier to trade than underlying asset

Exercise of the option does not lead to delivery of the underlying asset

Futures options and futures usually trade on the same exchange

Futures options may entail lower transactions costs

8

European Futures OptionsEuropean futures options and spot options

are equivalent when futures contract matures at the same time as the option

It is common to regard European spot options as European futures options when they are valued in the over-the-counter markets


9


Put-Call Parity for European Futures Options (Equation 16.1, page 348)

Consider the following two portfolios:1. European call plus Ke-rT of cash

2. European put plus long futures plus cash equal to F0e-rT

They must be worth the same at time T so that

c + Ke-rT = p + F0 e-rT

10


Other Relations

F0 e-rT – K < C – P < F0 – Ke-rT

c > (F0 – K)e-rT

p > (F0 – K)e-rT

11


Growth Rates For Futures Prices A futures contract requires no initial

investment In a risk-neutral world the expected return

should be zero The expected growth rate of the futures

price is therefore zero The futures price can therefore be treated

like a stock paying a dividend yield of r This is consistent with the results we have

presented so far (put-call parity, bounds, binomial trees)

12

Valuing European Futures Options

We can use the formula for an option on a stock paying a dividend yield S0 = current futures price, F0

q = domestic risk-free rate, r Setting q = r ensures that the expected

growth of F in a risk-neutral world is zero The result is referred to as Black’s model

because it was first suggested in a paper by Fischer Black in 1976


13


How Black’s Model is Used in Practice

European futures options and spot options are equivalent when future contract matures at the same time as the otion.

This enables Black’s model to be used to value a European option on the spot price of an asset

One advantage of this approach is that income on the asset does not have to be estimated explicitly

14


Black’s Model (Equations 16.5 and 16.6, page 350)

The formulas for European options on futures are known as Black’s model

TdT

TKFd

TTKF

d

dNFdNKep

dNKdNFecrT

rT

10

2

01

102

210

2/2)/ln(

2/2)/ln(

)()(

)()(

where

15

Using Black’s Model Instead of Black-Scholes (Example 16.5, page 351)

Consider a 6-month European call option on spot gold

6-month futures price is 1240, 6-month risk-free rate is 5%, strike price is 1200, and volatility of futures price is 20%

Value of option is given by Black’s model with F0=12400, K=1200, r=0.05, T=0.5, and =0.2

It is 88.37Fundamentals of Futures and Options Markets, 9th Ed, Ch 16, Copyright © John C. Hull 2016

16


Futures Price = $33Option Price = $4

Futures Price = $28Option Price = $0

Futures price = $30Option Price=?

Binomial Tree Example

A 1-month call option on futures has a strike price of 29.

17


Consider the Portfolio: long D futuresshort 1 call option

Portfolio is riskless when 3D – 4 = –2D or D = 0.8

3D – 4

-2D

Setting Up a Riskless Portfolio

18


Valuing the Portfolio( Risk-Free Rate is 6% )

The riskless portfolio is: long 0.8 futuresshort 1 call option

The value of the portfolio in 1 month is –1.6

The value of the portfolio today is –1.6e – 0.06/12 = –1.592

19


Valuing the Option

The portfolio that is long 0.8 futuresshort 1 option

is worth –1.592The value of the futures is zeroThe value of the option must

therefore be 1.592

20


Generalization of Binomial Tree Example (Figure 16.2, page 353)

A derivative lasts for time T and is dependent on a futures price

F0d ƒd

F0u ƒuF0

ƒ

21


Generalization(continued)

Consider the portfolio that is long D futures and short 1 derivative

The portfolio is riskless when

D

ƒu dfF u F d0 0

F0u D F0 D – ƒu

F0d D F0D – ƒd

22



Value of the portfolio at time T is F0u D –F0D – ƒu

Value of portfolio today is – ƒHence

ƒ = – [F0u D –F0D – ƒu]e-rT

23



Substituting for D we obtainƒ = [ p ƒu + (1 – p )ƒd ]e–rT

where

dudp

1

24


American Futures Option Prices vs American Spot Option Prices

If futures prices are higher than spot prices (normal market), an American call on futures is worth more than a similar American call on spot. An American put on futures is worth less than a similar American put on spot

When futures prices are lower than spot prices (inverted market) the reverse is true

25

Futures Style Options (page 354-55)

A futures-style option is a futures contract on the option payoff

Some exchanges trade these in preference to regular futures options

The futures price for a call futures-style option is

The futures price for a put futures-style option is


)()( 210 dKNdNF

)()( 102 dNFdKN

26


Put-Call Parity Results: Summary

:Futures

:exchangeForeign

:Indices

:Stock Paying dNondividen

0

0

0

0

rTrT

TrrT

qTrT

rT

eFpKec

eSpKec

eSpKec

SpKec

f

27


Summary of Key Results from Chapters 15 and 16

We can treat stock indices, currencies, & futures like a stock paying a continuous dividend yield of qFor stock indices, q = average

dividend yield on the index over the option life

For currencies, q = rƒ

For futures, q = r28

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Futures Options - OER University - Anvari.Netcbafaculty.org/Futures and Options... · PPT file · Web view · 2017-04-18Futures Options and Black’s Model. Chapter 16. Options